
\section{Motivating Application: Building Heating, Ventilation, and Air
Conditioning control}

\label{sec:motivation}

The building sector consumes about 40\% of the energy used in the United States
and is responsible for nearly 40\% of greenhouse gas emissions~\cite{UTRC}. It
is therefore economically, socially, and environmentally significant to reduce
the energy consumption of buildings. Building heating, ventilation, and air
conditioning systems make up a majority of this energy consumption.
In~\cite{UCmerced},~\cite{COBEE}, the authors have implemented MPC on building
heating, ventilation, and air conditioning (HVAC) systems obtaining reduced peak
power consumption and reduced overall energy usage compared to existing
production logic.

A building HVAC system is responsible for maintaining temperature and pressure
throughout a building. Figure \ref{fig:SystemModel} presents a schematic of a
typical building HVAC system. A building is representationally split up into
zones, which can be thought of as spaces that are serviced by the same air duct
output.  Generally, the system control inputs are cooling coils, heating coils,
and fan speeds. Many temperature and pressure measurements are made throughout
the building as well. 

\begin{figure}
\includegraphics[width=\columnwidth]{figures/ModelTol-eps-converted-to.pdf}
  \caption{System Scheme}
  \label{fig:SystemModel}
\end{figure}


Large-scale buildings will have many zones, and therefore many inputs and
outputs to the system. This increases complexity of the system.


